You can see that the word is always moving and pushed to the left.
I don't want it to do that, so how can I fix this?
I have also tried using the "Anchor Point" option to make it to the Center Left, but for some reason, when previewing the video, it does not do anything.

Ok, I've uploaded an example veg file, hope you have Vegas 12 or better. If not let me know and I will make a veg file in a lower version. Let me know if this works for you.
Russ Froze8272_typeontext.veg.zip

Yeah that works too. I've been modifying and playing with the file since I created it, you know just to see. I'm actually impressed what one can accomplish with just the legacy text and Vegas default Plugins. Yes if keyframe interpolation is left at default, the letters will tween between keyframes. You can select all the keyframes and change them all at once to see for yourself what the effects are.
Good Luck with your project.
Russ Froze